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Ranger 8

Ranger 8

Ranger 8 was designed to achieve a lunar impact trajectory and to transmit high-resolution photographs of the lunar surface during the final minutes of flight up to impact. The spacecraft carried six television vidicon cameras, 2 wide angle (channel F, cameras A and B) and 4 narrow angle (channel P) to accomplish these objectives. The cameras were arranged in two separate chains, or channels, each self-contained with separate power supplies, timers, and transmitters so as to afford the greatest reliability and probability of obtaining high-quality video pictures. No other experiments were carried on the spacecraft.

Spacecraft design

Rangers 6, 7, 8, and 9 were the so-called Block 3 versions of the Ranger spacecraft. The spacecraft consisted of a hexagonal aluminum frame base 1.5 m across on which was mounted the propulsion and power units, topped by a truncated conical tower which held the TV cameras. Two solar panel wings, each 739 mm wide by 1537 mm long, extended from opposite edges of the base with a full span of 4.6 m, and a pointable high gain dish antenna was hinge mounted at one of the corners of the base away from the solar panels. A cylindrical quasiomnidirectional antenna was seated on top of the conical tower. The overall height of the spacecraft was 3.6 m. Propulsion for the mid-course trajectory correction was provided by a 224 N thrust monopropellant hydrazine engine with 4 jet-vane vector control. Orientation and attitude control about 3 axes was enabled by 12 nitrogen gas jets coupled to a system of 3 gyros, 4 primary Sun sensors, 2 secondary Sun sensors, and an Earth sensor. Power was supplied by 9792 Si solar cells contained in the two solar panels, giving a total array area of 2.3 square meters and producing 200 W. Two 1200 watt.hour AgZnO batteries rated at 26.5 V with a capacity for 9 hours of operation provided power to each of the separate communication/TV camera chains. Two 1000 watt.hour AgZnO batteries stored power for spacecraft operations. Communications were through the quasiomnidirectional low-gain antenna and the parabolic high-gain antenna. Transmitters aboard the spacecraft included a 60 W TV channel F at 959.52 MHz, a 60 W TV channel P at 960.05 MHz, and a 3 W transponder channel 8 at 960.58 MHz. The telecommunications equipment converted the composite video signal from the camera transmitters into an RF signal for subsequent transmission through the spacecraft high-gain antenna. Sufficient video bandwidth was provided to allow for rapid framing sequences of both narrow- and wide-angle television pictures.

Mission Profile

The Atlas 196D and Agena B 6006 boosters performed nominally, injecting the Agena and Ranger 8 into an Earth parking orbit at 185 km altitude 7 minutes after launch. Fourteen minutes later a 90 second burn of the Agena put the spacecraft into lunar transfer trajectory, and several minutes later the Ranger and Agena separated. The Ranger solar panels were deployed, attitude control activated, and spacecraft transmissions switched from the omniantenna to the high-gain antenna by 21:30 UT. On 18 February at a distance of 160,000 km from Earth the planned mid-course maneuver took place, involving reorientation and a 59 second rocket burn. During the 27 minute maneuver, spacecraft transmitter power dropped severely, so that lock was lost on all telemetry channels. This continued intermittently until the rocket burn, at which time power returned to normal. The telemetry dropout had no serious effects on the mission. A planned terminal sequence to point the cameras more in the direction of flight just before reaching the Moon was cancelled to allow the cameras to cover a greater area of the Moon's surface. Ranger 8 reached the Moon on February 20 1965. The first image was taken at 9:34:32 UT at an altitude of 2510 km. Transmission of 7,137 photographs of good quality occurred over the final 23 minutes of flight. The final image taken before impact has a resolution of 1.5 meters. The spacecraft encountered the lunar surface in a direct hyperbolic trajectory, with incoming asymptotic direction at an angle of -13.6 degrees from the lunar equator. The orbit plane was inclined 16.5 degrees to the lunar equator. After 64.9 hours of flight, impact occurred at 09:57:36.756 UT on 20 February 1965 in Mare Tranquillitatis at approximately 2.67 degrees N, 24.65 degrees E. (The impact site is listed as about 2.72 N, 24.61 E in the initial report "Ranger 8 Photographs of the Moon".) Impact velocity was slightly less than 2.68 km/s. The spacecraft performance was excellent.

External link


- [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19780007206_1978007206.pdf Lunar impact: A history of Project Ranger (PDF) 1977] 8

Spacecraft

, 2004.]] A spacecraft is a vehicle that travels through space. Spacecraft include robotic or unmanned space probes as well as manned vehicles. The term is sometimes also used to describe artificial satellites, which have similar design criteria.

Overview

The term spaceship is generally applied only to spacecraft capable of transporting people. A space suit has at times been called a miniature spacecraft or spaceship, emphasizing its purpose of keeping its wearer alive while traveling in the vacuum of outer space. The spacecraft is one of the primal elements in science fiction. Numerous short stories and novels are built up around various ideas for spacecraft. Some hard science fiction books focus on the technical details of the craft, while others treat the spacecraft as a given and delve little into its actual implementation.

Examples of past or existing spacecraft

Manned
- Apollo Spacecraft
- Gemini Spacecraft
- International Space Station
- Mir
- Mercury Spacecraft
- Shuttle Buran
- Shenzhou Spacecraft
- Space Shuttle
- Soyuz Spacecraft
- SpaceShipOne
- Voskhod Spacecraft
- Vostok Spacecraft Unmanned
- Cassini-Huygens
- Cluster
- Deep Space 1
- Genesis
- Mars Exploration Rover
- Mars Global Surveyor
- Mars Pathfinder
- Pioneer 10
- Pioneer 11
- Progress
- SOHO
- Stardust
- Viking 1
- Viking 2
- Voyager 1
- Voyager 2
- WMAP

Spacecraft under development


- Crew Exploration Vehicle
- Kliper
- Automated Transfer Vehicle
- H-II Transfer Vehicle
- Ansari X Prize (incl. a list of spacecraft in various stages of completion as of 2005) The US Space Command, according to its "Long Range Plan", is currently planning to develop a weaponized spaceship, which has yet to be announced.[http://www.fas.org/spp/military/docops/usspac/]

See also


- Attitude control
- Expendable launch system
- Human spaceflight
- List of fictional spaceships
- List of spacecraft
- Spacecraft propulsion
- Space shuttle
- Starship
- Thruster
- Unidentified flying object
- Unmanned space mission

External links


- [http://science.hq.nasa.gov/missions/phase.html NASA: Space Science Spacecraft Missions]
- [http://www.skyrocket.de/space/ Gunter's Space Page - Complete information on spacecraft]
- [http://www.cinespaceships.net/ Cinespaceships - Database on spaceships in movie]
- ja:宇宙船

Ranger program

The Ranger program of unmanned space missions was the first United States attempt to obtain close-up images of the lunar surface. The Ranger spacecraft were designed to fly straight down towards the Moon and send images back until the moment of impact. Ranger was originally designed, beginning in 1959, in three distinct phases, called "blocks." Each block had different mission objectives and progressively more advanced system design. The JPL mission designers planned multiple launches in each block, to maximize the engineering experience and scientific value of the mission and to assure at least one successful flight. Total research, development, launch, and support costs for the Ranger series of spacecraft (Rangers 1 through 9) was approximately $170 million.

Block 1 missions

JPL Block 1, consisting of two spacecraft launched into Earth orbit in 1961, was intended to test the Atlas/Agena launch vehicle and spacecraft equipment without attempting to reach the Moon. Most elements of spacecraft technology taken for granted today were untested before Ranger. Perhaps the most important of these was three-axis attitude stabilization, meaning that the spacecraft is fixed in relation to space instead of being stabilized by spinning. This would permit pointing large solar panels at the Sun, a large antenna at Earth, and cameras and other directional scientific sensors at their appropriate targets. Rocket propulsion carried aboard the spacecraft was another critically important new technology, needed for accurate targeting at the Moon or distant planets. In addition, two-way communication and closed-loop tracking, requiring spacecraft and ground system development, and the use of on-board computing and sequencing combined with commands from the ground, all had to be developed and tried out in flight. Unfortunately, problems with the early version of the launch vehicle left Ranger 1 and Ranger 2 in short-lived, low-Earth orbits in which the spacecraft could not stabilize themselves, collect solar power, or survive for long.

Block 2 missions

Ranger 2 Block 2 of the Ranger project launched three spacecraft to the Moon in 1962, carrying a TV camera, a radiation detector, and a seismometer in a separate capsule slowed by a rocket motor and packaged to survive its low-speed impact on the Moon’s surface. The three missions together demonstrated good performance of the Atlas/Agena B launch vehicle and the adequacy of the spacecraft design, but unfortunately not all on the same attempt. Ranger 3 was launched into deep space, but an inaccuracy put it off course and it missed the Moon entirely. Ranger 4 had a perfect launch, but the spacecraft was completely disabled. The project team tracked the seismometer capsule to impact just out of sight on the lunar far side, validating the communications and navigation system. Ranger 5 missed the Moon and was disabled. No significant science information was gleaned from these missions. The craft weighed 331 kg.

Block 3 missions

Ranger's Block 3 embodied four launches in 1964-65. These spacecraft boasted a television instrument designed to observe the lunar surface during the approach; as the spacecraft neared the Moon, they would reveal detail smaller than the best Earth telescopes could show, and finally details down to dishpan size. The first of the new series, Ranger 6, had a flawless flight, except that the television system was disabled by an in-flight accident and could take no pictures. Ranger 6 The next three Rangers, with a redesigned television, were completely successful. Ranger 7 photographed its way down to target in a lunar plain, soon named Mare Cognitum, south of Copernicus crater. It sent more than 4,300 pictures from six cameras to waiting scientists and engineers. The new images revealed that craters caused by impact were the dominant features of the Moon's surface, even in the seemingly smooth and empty plains. Great craters were marked by small ones, and the small with tiny impact pockmarks, as far down in size as could be discerned -- about 50 centimeters (16 inches). The light-colored streaks radiating from Copernicus and a few other large craters turned out to be chains and nets of small craters and debris blasted out in the primary impacts. In February 1965, Ranger 8 swept an oblique course over the south of Oceanus Procellarum and Mare Nubium, to crash in Mare Tranquillitatis where Apollo 11 would land 4½ years later. It garnered more than 7,000 images, covering a wider area and reinforcing the conclusions from Ranger 7. About a month later, Ranger 9 came down in the 90 km diameter (75 mile) crater Alphonsus. Its 5,800 images, nested concentrically and taking advantage of very low-level sunlight, provided strong confirmation of the crater-on-crater, gently rolling contours of the lunar surface. Thus, after a long trouble-plagued start that taught the system engineers a great deal and the scientists virtually nothing, Project Ranger finished with three flights that greatly advanced the lunar scientists' knowledge of the surface and whetted their appetites for a closer look.

The Ranger spacecraft

Each Ranger spacecraft had 6 cameras on board. The cameras were fundamentally the same with differences in exposure times, fields of view, lenses, and scan rates. The camera system was divided into two channels, P (partial) and F (full). Each channel was self-contained with separate power supplies, timers, and transmitters. The F-channel had 2 cameras: the wide-angle A-camera and the narrow angle B-camera. The P-channel had four cameras: P1 and P2 (narrow angle) and P3 and P4 (wide angle). The final F-channel image was taken between 2.5 and 5 s before impact (altitude about 5 km) and the last P-channel image 0.2 to 0.4 s before impact (altitude about 600 m). The images provided better resolution than was available from Earth based views by a factor of 1000. Total research, development, launch, and support costs for the Ranger series of spacecraft (Rangers 1 through 9) was approximately $170 million.

Mission list


- Block 1
  - Ranger 1, launched 23 August 1961, lunar prototype, launch failure
  - Ranger 2, launched 18 November 1961, lunar prototype, launch failure
- Block 2
  - Ranger 3, launched 26 January 1962, lunar probe, spacecraft failed, missed moon
  - Ranger 4, launched 23 April 1962, lunar probe, spacecraft failed, impact
  - Ranger 5, launched 18 October 1962, lunar probe, spacecraft failed, missed
- Block 3
  - Ranger 6, launched 30 January 1964, lunar probe, impact, cameras failed
  - Ranger 7
    - Launched 28 July 1964
    - Impacted Moon 31 July 1964 at 13:25:49 UT
    - Latitude 10.35 S, Longitude 339.42 E - Mare Cognitum
  - Ranger 8
    - Launched 17 February 1965
    - Impacted Moon 20 February 1965 at 09:57:37 UT
    - Latitude 2.67 N, Longitude 24.65 E - Mare Tranquillitatis (Sea of Tranquility)
  - Ranger 9
    - Launched 21 March 1965
    - Impacted Moon 24 March 1965 at 14:08:20 UT
    - Latitude 12.83 S, Longitude 357.63 E - Alphonsus crater

External links


- [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19780007206_1978007206.pdf Lunar Impact: A History of Project Ranger (PDF) 1977]
- [http://history.nasa.gov/SP-4210/pages/Cover.htm Lunar Impact: A History of Project Ranger (HTML)] Both links lead to a whole book on the program. For the HTML one, scroll down to see the table of contents link.

See also


- Surveyor program
- Lunar Orbiter program
- Apollo program
- Luna programme
- [http://wikisource.org/wiki/NASA_FACTS_Volume_2_number_6_PROJECT_RANGER NASA_FACTS_Volume_2_number_6_PROJECT_RANGER on wikisource]
-

Aluminium

x Aluminium or aluminum (Symbol Al) (see the spelling section below) is a silvery and ductile member of the poor metal group of chemical elements. Its atomic number is 13. Aluminium is found primarily as the ore bauxite and is remarkable for its resistance to oxidation (due to the phenomenon of passivation), its strength, and its light weight. Aluminium is used in many industries to make millions of different products and is very important to the world economy. Structural components made from aluminium are vital to the aerospace industry and very important in other areas of transportation and building in which light weight, durability, and strength are needed.

Properties

transport Aluminium is a soft and lightweight metal with a dull silvery appearance, due to a thin layer of oxidation that forms quickly when it is exposed to air. Aluminium is nontoxic (as the metal) nonmagnetic and non-sparking. Pure aluminium has a tensile strength of about 49 megapascals (MPa) and 700 MPa if it is formed into an alloy. Aluminium is about one-third as dense as steel or copper; is malleable, ductile, and easily machined and cast; and has excellent corrosion resistance and durability due to the protective oxide layer. It is also nonmagnetic and nonsparking and is the second most malleable metal (after gold) and the sixth most ductile. ductile

Applications

Whether measured in terms of quantity or value, the use of aluminium exceeds that of any other metal except iron, and it is important in virtually all segments of the world economy. Pure aluminium has a low tensile strength, but readily forms alloys with many elements such as copper, zinc, magnesium, manganese and silicon. When combined with thermo-mechanical processing these aluminium alloys display a marked improvement in mechanical properties. Aluminium alloys form vital components of aircraft and rockets as a result of their high strength to weight ratio. When aluminium is evaporated in a vacuum it forms a coating that reflects both visible light and radiant heat. These coatings form a thin layer of protective aluminium oxide that does not deteriorate as silver coatings do. In particular, nearly all modern mirrors are made using a thin reflective coating of aluminium on the back surface of a sheet of float glass. Telescope mirrors are also coated with a thin layer of aluminium, but are front coated to avoid internal reflections even though this makes the surface more susceptible to damage. Telescope Diet Coke.]] Some of the many uses for aluminium are in:
- Transportation (automobiles, airplanes, trucks, railroad cars, marine vessels, etc.)
- Packaging (cans, foil, etc.)
- Water treatment
- Construction (windows, doors, siding, building wire, etc.
- Consumer durable goods (appliances, cooking utensils, etc.)
- Electrical transmission lines (aluminium conductors are half the weight of copper for equal conductivity and lower in price[http://www.metalprices.com])
- Machinery.
- Although non-magnetic itself, aluminium is used in MKM steel and Alnico magnets.
- Super purity aluminium (SPA, 99.980% to 99.999% Al) is used in electronics and CDs.
- Powdered aluminium is commonly used for silvering in paint. Aluminium flakes may also be included in undercoat paints, particularly wood primer — on drying, the flakes overlap to produce a water resistant barrier.
- Anodised aluminium is more stable to further oxidation, and is used in various fields of construction.
- Most modern computer CPU heat sinks are made of aluminium due to its ease of manufacture and good heat conductivity. Copper heat sinks are smaller although more expensive and harder to manufacture. Aluminium oxide, alumina, is found naturally as corundum (rubies and sapphires), emery, and is used in glass making. Synthetic ruby and sapphire are used in lasers for the production of coherent light. Aluminium oxidises very energetically and as a result has found use in solid rocket fuels, thermite, and other pyrotechnic compositions. Aluminium is also a superconductor, with a superconduting critical temperature of 1.2 Kelvin.

Engineering use

Improper use of aluminium can result in problems, particularly in contrast to iron or steel, which appear "better behaved" to the intuitive designer, mechanic, or technician. The reduction by two thirds of the weight of an aluminium part compared to a similarly sized iron or steel part seems enormously attractive, but it should be noted that it is accompanied by a reduction by two thirds in the stiffness of the part. Therefore, although direct replacement of an iron or steel part with a duplicate made from aluminium may still give acceptable strength to withstand peak loads, the increased flexibility will cause three times more deflection in the part. Where failure is not an issue but excessive flex is undesirable due to requirements for precision of location or efficiency of transmission of power, simple replacement of steel tubing with similarly sized aluminium tubing will result in a degree of flex which is undesirable; for instance, the increased flex under operating loads caused by replacing steel bicycle frame tubing with aluminium tubing of identical dimensions will cause misalignment of the power-train as well as absorbing the operating force. To increase the rigidity by increasing the thickness of the walls of the tubing increases the weight proportionately, so that the advantages of lighter weight are lost as the rigidity is restored. Aluminium can best be used by redesigning the part to suit its characteristics; for instance making a bicycle of aluminium tubing which has an oversize diameter rather than thicker walls. In this way, rigidity can be restored or even enhanced without increasing weight. The limit to this process is the increase in susceptibility to what is termed "crippling" failure, where the deviation of the force from any direction other than directly along the axis of the tubing causes folding of the walls of the tubing. For instance, a common aluminium soft drink can should be able to support an enormous weight directly along its axis; in practice, however, the walls of the can buckle, crumple, and/or fold up under even a mild force, due to minute deviations from the precise axial direction, making possible the common pastime of flattening an empty can by slamming it against one's forehead. The latest models of the Corvette automobile, among others, are a good example of redesigning parts to make best use of aluminium's advantages. The aluminium chassis members and suspension parts of these cars have large overall dimensions for stiffness but are lightened by reducing cross-sectional area and removing unneeded metal; as a result, they are not only equally or more durable and stiff as the usual steel parts, but they possess an airy gracefulness which most people find attractive. Similarly, aluminium bicycle frames can be optimally designed so as to provide rigidity where required, yet have flexibility in terms of absorbing the shock of bumps from the road and not transmitting them to the rider. The strength and durability of aluminium varies widely, not only as a result of the components of the specific alloy, but also as a result of the particular manufacturing process; for this reason, it has from time to time gained a bad reputation. For instance, a high frequency of failure in many early aluminium bicycle frames in the 1970s resulted in just such a poor reputation; with a moment's reflection, however, the widespread use of aluminium components in the aerospace and automotive high performance industries, where huge stresses are undergone with vanishingly small failure rates, proves that properly built aluminium bicycle components should not be unusually unreliable, and this has subsequently proved to be the case. Similarly, use of aluminium in automotive applications, particularly in engine parts which must survive in difficult conditions, has benefited from development over time. An Audi engineer commented about the V12 engine, producing over 500 horsepower (370 kW), of an Auto Union race car of the 1930s which was recently restored by the Audi factory, that the aluminium alloy of which the engine was constructed would today be used only for lawn furniture and the like. Even the aluminium cylinder heads and crankcase of the Corvair, built as recently as the 1960s, earned a reputation for failure and stripping of threads in holes, even as large as spark plug holes, which is not seen in current aluminium cylinder heads. Often, aluminium's sensitivity to heat must also be considered. Even a relatively routine procedure such as welding is complicated by the fact that aluminium will melt long before it gets even dully red hot; therefore, unlike steel or iron, where the experienced welder can know from its hue how close the metal is to the melting point, welding aluminium requires a degree of expertise incorporating an almost intuitive sense of the metal's temperature, or else the part suddenly and without warning melts into a puddle. Aluminium also will accumulate internal stresses and strains under conditions of overheating; while not immediately obvious, the tendency of the metal to "creep" under sustained stresses results in delayed distortions, for instance the commonly observed warping or cracking of aluminium automobile cylinder heads after an engine is overheated, sometimes as long as years later, or the tendency of welded aluminium bicycle frames to gradually twist out of alignment from the stresses accumulated during the welding process. For this reason, many uses of aluminium in the aerospace industry avoid heat altogether by joining parts using adhesives; this was also used for some of the early aluminium bicycle frames in the 1970s, with unfortunate results when the aluminium tubing corroded slightly, loosening the bond of the adhesive and leading to failure of the frame. Stresses from overheating aluminium can be relieved by heat-treating the parts in an oven and gradually cooling, in effect annealing the stresses; this can also result, however, in the part becoming distorted as a result of these stresses, so that such heat-treating of welded bicycle frames, for instance, results in a significant fraction becoming misaligned. If the misalignment is not too severe, once cooled they can be bent back into alignment with no negative consequences; of course, if the frame is properly designed for rigidity (see above), this will require enormous force.

Household wiring

Because of its high conductivity and relatively low price compared to copper at the time, aluminium was introduced for household electrical wiring to a large degree in the United States in the 1960s. Unfortunately, many of the wiring fixtures at the time were not designed to accept aluminium wire. More specifically:
- The greater coefficient of thermal expansion of aluminium, causes the wire to expand and contract relative to the dissimilar metal screw connection, eventually loosening the connection.
- Pure aluminium has a tendency to "creep" under steady sustained pressure (to a greater degree as the temperature rises), again producing a degree of looseness in an initially tight connection.
- Galvanic corrosion from the dissimilar metals increases the electrical resistance of the connection. In combination, these properties caused connections between electrical fixtures and aluminium wiring to overheat which resulted in several fires. As a result, aluminium household wiring has become unpopular, and in many jurisdictions is not permitted in very small sizes in new construction. However, aluminium wiring can be safely used with fixtures whose connections are designed to avoid loosening and overheating. Older fixtures of this type are marked "Al/Cu", and newer ones are marked "CO/ALR". Otherwise, aluminium wiring can be terminated by crimping it to a short "pigtail" of copper wire, which can be treated as any other copper wire. A properly done crimp, requiring high pressure produced by the proper tool, is tight enough not only to eliminate any thermal expansion of the aluminium, but also to exclude any atmospheric oxygen and thus prevent corrosion between dissimilar metals. New alloys are used for aluminium building wire today in combination with aluminium terminations. Connections made with these standard industry products are as safe and reliable as copper connections. :See also:Aluminum wire

History

The oldest suspected (although unprovable) reference to aluminium is in Pliny the Elder's Naturalis Historia: One day a goldsmith in Rome was allowed to show the Emperor Tiberius a dinner plate of a new metal. The plate was very light, and almost as bright as silver. The goldsmith told the Emperor that he had produced the metal from ordinary clay. He also assured the Emperor that only he, himself, and the gods knew how to produce this metal from clay. The Emperor became very interested, and, as a financial expert, he was also worried. He feared that all his treasures of gold and silver would fall in value if people started producing this bright metal from clay. Therefore, instead of giving the goldsmith the recognition the latter had anticipated, he ordered him to be beheaded. [http://www.findarticles.com/p/articles/mi_m2843/is_n3_v19/ai_16836663 Notes] - [http://www.world-aluminium.org/history/antiquity.html Source] The ancient Greeks and Romans used salts of this metal as dyeing mordants and as astringents for dressing wounds, and alum is still used as a styptic. Further Joseph Needham suggested finds in 1974 showed the ancient Chinese used aluminium (see the link for "Notes" above). In 1761 Guyton de Morveau suggested calling the base alum 'alumine'. In 1808, Humphry Davy identified the existence of a metal base of alum, which he named (see Spelling below for more information on the name). Friedrich Wöhler is generally credited with isolating aluminium (Latin alumen, alum) in 1827 by mixing anhydrous aluminium chloride with potassium. However, the metal had been produced for the first time two years earlier in an impure form by the Danish physicist and chemist Hans Christian Ørsted. Therefore almanacs and chemistry sites often list Øersted as the discoverer of aluminium.[http://www.chemicalelements.com/elements/al.html#isotopes Source] Still it would further be P. Berthier who discovered aluminium in bauxite ore and successfully extracted it. The Frenchman Henri Saint-Claire Deville improved Wöhler's method in 1846 and described his improvements in a book in 1859, chief among these being the substitution of sodium for the considerably more expensive potassium. The American Charles Martin Hall of Oberlin, OH applied for a patent (400655) in 1886 for an electrolytic process to extract aluminium using the same technique that was independently being developed by the Frenchman Paul Héroult in Europe. The invention of the Hall-Héroult process in 1886 made extracting aluminium from minerals cheaper, and is now the principal method in common use throughout the world. Upon approval of his patent in 1889, Hall, with the financial backing of Alfred E. Hunt of Pittsburgh, PA, started the Pittsburgh Reduction Company, renamed to Aluminum Company of America in 1907, later shortened to Alcoa. Alcoa Aluminium was selected as the material to be used for the apex of the Washington Monument, at a time when one ounce cost twice the daily wages of a common worker in the project. [http://www.tms.org/pubs/journals/JOM/9511/Binczewski-9511.html Source] Germany became the world leader in aluminium production soon after Adolf Hitler seized power. By 1942, however, new hydroelectric power projects such as the Grand Coulee Dam gave the United States something Nazi Germany could not hope to compete with, namely the capability of producing enough aluminium to manufacture sixty thousand warplanes in four years. [http://www.phpsolvent.com/wordpress/?page_id=341]

Natural occurrence

Although aluminium is an abundant element in Earth's crust (believed to be 7.5% to 8.1%), it is very rare in its free form and was once considered a precious metal more valuable than gold. Napoleon III of France had a set of aluminium plates reserved for his finest guests. Others had to make do with gold ones. Aluminium has been produced in commercial quantities for just over 100 years. Aluminium was, when it was first discovered, extremely difficult to separate from its ore. Aluminium is among the most difficult metals on earth to refine, despite the fact that it is one of the planet's most common. The reason is that aluminium is oxidised very rapidly and that its oxide is an extremely stable compound that, unlike rust on iron, does not flake off. The very reason for which aluminium is used in many applications is why it is so hard to produce. Recovery of this metal from scrap (via recycling) has become an important component of the aluminium industry. Recycling involves simply melting the metal, which is far less expensive than creating it from ore. Refining aluminium requires enormous amounts of electricity; recycling it requires only 5% of the energy to produce it. A common practice since the early 1900s, aluminium recycling is not new. It was, however, a low-profile activity until the late 1960s when the exploding popularity of aluminium beverage cans finally placed recycling into the public consciousness. Other sources for recycled aluminium include automobile parts, windows and doors, appliances, containers and other products. Aluminium is a reactive metal and it is hard to extract it from its ore, aluminium oxide (Al2O3). Direct reduction, with carbon for example, is not economically viable since aluminium oxide has a melting point of about 2000°C. Therefore, it is extracted by electrolysis — the aluminium oxide is dissolved in molten cryolite and then reduced to the pure metal. By this process, the actual operational temperature of the reduction cells is around 950 to 980°C. Cryolite was originally found as a mineral on Greenland, but has been replaced by a synthetic cryolite. Cryolite is a mixture of aluminium, sodium, and calcium fluorides: (Na3AlF6). The aluminium oxide (a white powder) is obtained by refining bauxite, which is red since it contains 30 to 40% iron oxide. This is done using the so-called Bayer process. Previously, the Deville process was the predominant refining technology. The electolytic process replaced the Wöhler process, which involved the reduction of anhydrous aluminium chloride with potassium. Both of the electrodes used in the electrolysis of aluminium oxide are carbon. Once the ore is in the molten state, its ions are free to move around. The reaction at the negative cathode is :Al3+ + 3e- → Al Here the aluminium ion is being reduced (electrons are added). The aluminium metal then sinks to the bottom and is tapped off. At the positive electrode (anode) oxygen gas is formed: :2O2- → O2 + 4e- This carbon anode is then oxidised by the oxygen. The anodes in a reduction must therefore be replaced regularly, since they are consumed in the process: :O2 + C → CO2 Contrary to the anodes, the cathodes are not consumed during the operation, since there is no oxygen present at the cathode. The carbon cathode is protected by the liquid aluminium inside the cells. Cathodes do erode, mainly due to electrochemical processes. After 5 to 10 years, depending on the current used in the electrolysis, a cell has to be reconstructed completely, because the cathodes are completely worn. Aluminium electrolysis with the Hall-Héroult process consumes a lot of energy, but alternative processes were always found to be less viable economically and/or ecologically. The world-wide average specific energy consumption is approximately 15±0.5 kilowatt-hours per kilogram of aluminium produced (52 to 56 MJ/kg). The most modern smelters reach approximately 12.8 kW·h/kg (46.1 MJ/kg). Reduction line current for older technologies are typically 100 to 200 kA. State-of-the-art smelters operate with about 350 kA. Trials have been reported with 500 kA cells. Electric power represents about 20 to 40% of the cost of producing aluminium, depending on the location of the aluminium smelter. Smelters tend to be located where electric power is plentiful and inexpensive, such as South Africa, the South Island of New Zealand, Australia, China, Middle-East, Russia, Iceland and Quebec in Canada. China is currently (2004) the top world producer of aluminium. Suriname depends on aluminium exports for 70% of its export earnings.[http://www.cia.gov/cia/publications/factbook/geos/ns.html#Econ]

Isotopes

Aluminium has nine isotopes, whose mass numbers range from 23 to 30. Only Al-27 (stable isotope) and Al-26 (radioactive isotope, t1/2 = 7.2 × 105 y) occur naturally, however Al-27 has a natural abundance of 100%. Al-26 is produced from argon in the atmosphere by spallation caused by cosmic-ray protons. Aluminium isotopes have found practical application in dating marine sediments, manganese nodules, glacial ice, quartz in rock exposures, and meteorites. The ratio of Al-26 to beryllium-10 has been used to study the role of transport, deposition, sediment storage, burial times, and erosion on 105 to 106 year time scales. Cosmogenic Al-26 was first applied in studies of the Moon and meteorites. Meteorite fragments, after departure from their parent bodies, are exposed to intense cosmic-ray bombardment during their travel through space, causing substantial Al-26 production. After falling to Earth, atmospheric shielding protects the meteorite fragments from further Al-26 production, and its decay can then be used to determine the meteorite's terrestrial age. Meteorite research has also shown that Al-26 was relatively abundant at the time of formation of our planetary system. Possibly, the energy released by the decay of Al-26 was responsible for the remelting and differentiation of some asteroids after their formation 4.6 billion years ago.

Clusters

In the journal Science of 14 January 2005 it was reported that clusters of 13 aluminium atoms (Al13) had been made to behave like an iodine atom; and, 14 aluminium atoms (Al14) behaved like an alkaline earth atom. The researchers also bound 12 iodine atoms to an Al13 cluster to form a new class of polyiodide. This discovery is reported to give rise to the possibility of a new characterisation of the periodic table: superatoms. The research teams were led by Shiv N. Khanna (Virginia Commonwealth University) and A. Welford Castleman Jr (Penn State University). [http://www.science.psu.edu/alert/Castleman1-2005.htm]

Precautions

Aluminium is one of the few abundant elements that appears to have no beneficial function in living cells, but a few percent of people are allergic to it — they experience contact dermatitis from any form of it: an itchy rash from using styptic or antiperspirant products, digestive disorders and inability to absorb nutrients from eating food cooked in aluminium pans, and vomiting and other symptoms of poisoning from ingesting such products as Rolaids , Amphojel, and Maalox (antacids). In other persons, aluminium is not considered as toxic as heavy metals, but there is evidence of some toxicity if it is consumed in excessive amounts, although the use of aluminium cookware, popular because of its corrosion resistance and good heat conduction, has not been shown to lead to aluminium toxicity in general. Excessive consumption of antacids containing aluminium compounds and excessive use of aluminium-containing antiperspirants are more likely causes of toxicity. It has been suggested that aluminium may be linked to Alzheimer's disease, although that research has recently been refuted; aluminium accumulation may be a consequence of the Alzheimer's damage, not the cause. In any event, if there is any toxicity of aluminium it must be via a very specific mechanism, since total human exposure to the element in the form of naturally occurring clay in soil and dust is enormously large over a lifetime. Care must be taken to prevent aluminium from coming into contact with certain chemicals that can cause it to corrode quickly. For example, just a small amount of mercury applied to the surface of a piece of aluminium can break up the normal aluminium oxide barrier usually present. Within a few hours, even a heavy structural beam can be significantly weakened. For this reason, mercury thermometers are not allowed on many airliners, as aluminium is a common structural component in aircraft.

Spelling

Etymology / Nomenclature history

In 1808, Humphry Davy originally proposed the name alumium while trying to isolate the new metal electrolytically from the mineral alumina. In 1812 he changed the name to aluminum to match its Latin root. The same year, an anonymous contributor to the Quarterly Review objected to aluminum, and proposed the name aluminium. :Aluminium, for so we shall take the liberty of writing the word, in preference to aluminum, which has a less classical sound. (Q. Review VIII. 72, 1812) This had the advantage of conforming to the -ium suffix precedent set by other newly discovered elements of the period: potassium, sodium, magnesium, calcium, and strontium (all of which Davy had isolated himself). Nevertheless, -um spellings for elements were not unknown at the time: platinum, which had been known to Europeans since the 16th century, molybdenum, which was discovered in 1778, and tantalum, which was discovered in 1802, all have spellings ending in -um. Curiously, the United States adopted the -ium for most of the 19th century with aluminium appearing in Webster's Dictionary of 1828. However in 1892 Charles Martin Hall used the -um spelling in an advertising handbill for his new efficient electrolytic method for the production of aluminium, despite using the -ium spelling in all of his patents filed between 1886 and 1903. It has consequently been suggested that the spelling on the flyer was a simple spelling mistake rather a deliberate choice to use the -um spelling. Hall's domination of production of the metal ensured that the spelling aluminum became the standard in North America, even though the Webster Unabridged Dictionary of 1913 continued to use the -ium version. In 1926, the American Chemical Society officially decided to use aluminum in its publications, and American dictionaries typically label the spelling aluminium as a British variant.

Present day spelling

In the English-speaking world, the spellings (and associated pronunciations) aluminium and aluminum are both in common use in both scientific and nonscientific contexts. In the United States, the spelling aluminium is largely unknown, and the spelling aluminum predominates. Elsewhere in the English-speaking world the spelling aluminium predominates, and the spelling aluminum is largely unknown. However, in Canada both spellings are common, due to the multiple influences on the language of its proximity to the United States, its British colonial past and the large number of native French speakers. Outside English, the "ium" spelling is widespread: the word is aluminium in French and German, and identical or similar forms are used in many other languages. Consequently it is the more common of the two spellings in global terms, even though there may be more users of aluminum in the English-speaking world. The International Union of Pure and Applied Chemistry (IUPAC) adopted aluminium as the standard international name for the element in 1990, but three years later recognised aluminum as an acceptable variant. Hence their periodic table includes both, but places aluminium first [http://www.iupac.org/reports/periodic_table/index.html]. IUPAC officially prefers the use of aluminium in its internal publications, although several IUPAC publications use the spelling aluminum.[http://www.iupac.org/cgi-bin/htsearch?sort=score&restrict=www.iupac.org%2Fpublications%2Fci&config=htdig&restrict=&exclude=www.iupac.org%2Fgoldbook%2F&words=aluminum&submit=]

Chemistry

Oxidation state 1


- AlH is produced when aluminium is heated at 1500 °C in an atmosphere of hydrogen.
- Al2O is made by heating the normal oxide, Al2O3, with silicon at 1800 °C in a vacuum.
- Al2S can be made by heating Al2S3 with aluminium shavings at 1300 °C in a vacuum. It quickly disproportionates to the starting materials. The selenide is made in a parallel manner.
- AlF, AlCl and AlBr exist in the gaseous phase when the tri-halide is heated with aluminium.

Oxidation state 2


- Aluminium suboxide, AlO can be shown to be present when aluminium powder burns in oxygen.

Oxidation state 3


- Fajans rules show that the simple trivalent cation Al3+ is not expected to be found in anhydrous salts or binary compounds such as Al2O3. The hydroxide is a weak base and aluminium salts of weak bases, such as carbonate, can't be prepared. The salts of strong acids, such as nitrate, are stable and soluble in water, forming hydrates with at least six molecules of water of crystallization.
- Aluminium hydride, (AlH3)n, can be produced from trimethylaluminium and an excess of hydrogen. It burns explosively in air. It can also be prepared by the action of aluminium chloride on lithium hydride in ether solution, but cannot be isolated free from the solvent.
- Aluminium carbide, Al4C3 is made by heating a mixture of the elements above 1000 °C. The pale yellow crystals have a complex lattice structure, and react with water or dilute acids to give methane. The acetylide, Al2(C2)3, is made by passing acetylene over heated aluminium.
- Aluminium nitride, AlN, can be made from the elements at 800 °C. It is hydrolysed by water to form ammonia and aluminium hydroxide.
- Aluminium phosphide, AlP, is made similarly, and hydrolyses to give phosphine.
- Aluminium oxide, Al2O3, occurs naturally as corundum, and can be made by burning aluminium in oxygen or by heating the hydroxide, nitrate or sulfate. As a gemstone, its hardness is only exceeded by diamond, boron nitride and carborundum. It is almost insoluble in water.
- Aluminium hydroxide may be prepared as a gelatinous precipitate by adding ammonia to an aqueous solution of an aluminium salt. It is amphoteric, being both a very weak acid, and forming aluminates with alkalis. It exists in various crystalline forms.
- Aluminium sulfide, Al2S3, may be prepared by passing hydrogen sulfide over aluminium powder. It is polymorphic.
- Aluminium fluoride, AlF3, is made by treating the hydroxide with HF, or can be made from the elements. It consists of a giant molecule which sublimes without melting at 1291 °C. It is very inert. The other trihalides are dimeric, having a bridge-like structure.
- Organo-metallic compounds of empirical formula AlR3 exist and, if not also giant molecules, are at least dimers or trimers. They have some uses in organic synthesis, for instance trimethylaluminium.
- Alumino-hydrides of the most electropositive elements are known, the most useful being lithium aluminium hydride, Li[AlH4]. It decomposes into lithium hydride, aluminium and hydrogen when heated, and is hydrolysed by water. It has many uses in organic chemistry. The aluminohalides have a similar structure.

Aluminium in popular culture


- In the film Star Trek IV: The Voyage Home, Scotty devises the fictional material transparent aluminum.

See also


- Alloys of aluminium.

References


- [http://periodic.lanl.gov/elements/13.html Los Alamos National Laboratory – Aluminum]
- [http://www.worldwidewords.org/articles/aluminium.htm World Wide Words] A history of the spelling of aluminium from a British viewpoint.
- Oxford English Dictionary Entries "aluminum" and "aluminium", available by subscription. [http://www.oed.com]

External links


- [http://www.webelements.com/webelements/elements/text/Al/index.html WebElements.com – Aluminium]
- [http://www.world-aluminium.org/ World Aluminium]
- [http://www.indexmundi.com/en/commodities/minerals/aluminum/aluminum_table12.html World production of primary aluminum, by country]
- [http://www.saanet.org/kashipur/docs/seenalum.htm Social and Environmental Impact of the Aluminium Industry]
- [http://153rd.com/sam/as/physics/aluminium/normal/redirect.html Sam's Aluminium Information Site] Patents
- US[http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=/netahtml/srchnum.htm&r=1&f=G&l=50&s1=400664.WKU.&OS=PN/400664&RS=PN/400664 400664] – Process of reducing aluminum from its floride salts by electrolysis – C. M. Hall Category:Chemical elements Category:Poor metals Category:Pigments Category:Pyrotechnic chemicals Category:Rocket fuels ko:알루미늄 ja:アルミニウム simple:Aluminium th:อะลูมิเนียม

Atlas rocket

The Atlas is a venerable line of space launch vehicles built by Lockheed Martin. Originally designed as an ICBM in the late 1950s, the Atlas is today used as a launch platform for commercial and military satellites, and other space vehicles.

History

The Atlas, first tested in 1959, was the United States' first successful ICBM (Intercontinental Ballistic Missile). It was a "1.5 stage", liquid-fueled (LOX and RP-1) rocket, with three engines producing 1,590 kN of thrust. Atlas was originally developed by the Convair company for the USAF with work on an intermediate range missle beginning in 1947. In 1955 the CIA learned that the Soviet ICBM programme was making progress so Atlas became a crash programme of the highest national importance. The missile was originally given the military designation "XB-65", thus making it a bomber; from 1955 it was redesignated "SM-65" and, from 1962, it became "CGM-16". This letter "C" stood for "coffin" or "Container", the rocket being stored in a hardened container; it was prepared for launch by being raised and fueled in the open. The Atlas-F (HGM-16) was stored vertically underground, but launched after being lifted to the surface. The Atlas never was used in a missile silo, deep underground. From the mid-1960s, the Atlas (and its 'bigger brother', the Titan) were phased out in favour of the LGM-30 Minuteman, a solid-fuelled rocket which could be stored for long periods and launched, without fuelling, at the turn of a key. Though never used in combat, the Atlas was used as the expendable launch system for the Mariner space probes used to study Mercury, Venus, and Mars (1962–1973); and to launch ten of the Mercury program missions (1962–1963). The Mercury-Atlas missions resulted in the first American to orbit the earth (Lt. Col. John H. Glenn Jr.) in February of 1962. (Major Yuri A. Gagarin, a Soviet cosmonaut, was the first human in orbit on April 12, 1961.) Atlas launched the Agena Target Vehicles used during the Gemini program. Direct Atlas descendants continue to be used as satellite launch vehicles into the 21st century. Atlas was suggested for use by the United States Air Force in what became known as Project Vanguard. This suggestion was ultimately turned down, however, as Atlas would not be operational in time and was seen by many as being too heavily connected to the military for use in the U.S.' IGY satellite attempt. Atlas, named for the Atlas of Greek mythology, got its start in 1946 with the award of a Army Air Forces research contract to Convair for the study of a 1,500 to 5,000 mi. (2,400 to 8,000 km) range nuclear armed missile. This was the MX-774 or Hiroc project. The contract was canceled in 1947 but the Army Air Forces allowed Convair to launch the three almost-completed research vehicles using the remaining contract funds. The three flights were only partially successful. However they did show that balloon tanks, and gimbaled rocket engines were valid concepts. 1947

Mercury-Atlas Three (Orbit Flight Events- April 25, 1961)


Design

Atlas is rare in its use of balloon tanks for fuel, made of very thin stainless steel with minimal or no rigid support structures. Pressure in the tanks provides the structural rigidity required for flight. An Atlas rocket will collapse under its own weight if not kept pressurized. The only other known use of balloon tanks at the time of writing is the Centaur high-energy upper stage. Atlas also has a unique and somewhat odd staging system. Most rockets stage by dropping both engines and fuel tanks. However, when the Atlas missile was being developed, there were considerable doubts as to whether or not a rocket motor could be ignited in space. Therefore, the decision was made to ignite all three of the Atlas' engines at launch - later, two of the engines would be discarded, while the third continued to burn. Rockets using this technique are sometimes called stage and a half boosters. This technique is made possible by the extremely light weight of the balloon tanks. The tanks make up such a small percentage of the total booster weight that the weight penalty of lifting them to orbit is not offset by the technical and weight penalty required to throw half of them away mid-flight. Depending on how you look at it, this makes Atlas a single-stage-to-orbit booster (though most call it a 1.5 stage to orbit).

Current Atlas Family


- Atlas II
- Atlas III
- Atlas V
- GX The Atlas II series had 63 successful flights with the last launched August 31, 2004, it is considered the most reliable launcher in the world. The newest version of Atlas, the Atlas V, is an Atlas in name alone as it contains little Atlas technology. It no longer uses balloon tanks nor 1.5 staging, but incorporates a rigid framework for its first stage booster much like the Titan family of vehicles. Ironically, given Atlas's origin as a military weapon, the Atlas III and Atlas V use Russian-designed engines. 2004 2004

External links


- [http://www.designation-systems.net/dusrm/m-16.html Atlas launch vehicle profile]
- [http://www.astronautix.com/lvs/atlasd.htm Atlas D] from Encyclopedia Astronautica
- [http://www.geocities.com/atlas_missile/ Atlas ICBM History site]
- [http://www.ilslaunch.com/atlas/atlasii/ Atlas II - Lockheed Martin]

Related content

Comparable missiles: SM-68 Titan Designation sequence: MGM-13 Mace - MIM-14 - RGM-15 - CGM-16/HGM-16 - PGM-17 - MGM-18 - PGM-19 Designation sequence: SM-62 - XGAM-63 - SM-64 - SM-65 - B-66 - GAM-67 - XB-68/SM-68 Related lists: List of missiles Category:Space launch vehicles Category:American Cold War intercontinental ballistic missiles Category:Mercury program ja:アトラス (ミサイル)

Agena

: For the Agena star, see Hadar. The Agena was a rocket upper stage developed by Lockheed for the ill-fated WS-117L US reconnaissance satellite program. It lived on to see extensive use as the upper stage/spacecraft for the Corona spy satellite program and as an upper stage on the Thor, Atlas, and Titan boosters. It was also used by the manned Gemini program to practice rendezvous and docking (see Agena Target Vehicle). Agena Target Vehicle It was 5 feet (1.5 m) in diameter, three axis stabilized (for the benefit of the reconnaissance system cameras) and its Bell 8096 engine produced 16,000 lbf (71 kN) thrust using hydrazine (UDMH) and nitrogen tetroxide as propellants. The engine could be restarted multiple times in orbit. This engine started life as the power plant for the canceled rocket-propelled nuclear warhead pod for the Convair B-58 Hustler bomber. Agena was thus known as Hustler early in its development. There were at least three versions of the Agena: ; A : 69 kN thrust Bell 8048 engine, 120 second burn time, used on Thor and Atlas. ; B : 71 kN thrust Bell 8081 engine, 240 second burn time, used on Thor and Atlas. Launched early SAMOS and MIDAS military satellites and the Ranger lunar probes. ; C : Proposed but never built. ; D : 71 kN thrust Bell 8096 engine, 265 second burn time, used on Thor, Atlas, and Titan. Launched early KH-7 GAMBIT spy satellites and the two Mariner Mars probes. As a military reconnaissance spacecraft, much information on the project remains classified. The final Agena launch was of an Agena D on 12 February 1987, configured as the upper stage of a Titan 34B [http://www.designation-systems.net/dusrm/app1/rm-81.html]. Category:Space launch vehicles



Altitude

For other uses see Altitude (disambiguation) Altitude is the elevation of an object from a known level or datum, called zero level. Most often this level is defined as the absolute sea level, but it can vary. In aviation, the term altitude is used to describe elevation above mean sea level, the term height refers to elevation above a ground reference point and the term flight level is the elevation according to a standard pressure altimeter setting. Atmospheric pressure decreases with altitude. In North America and the UK altitude is usually measured in feet. Everywhere else in the world the altitude is measured in metres.
- High altitude = 1500m – 3500m
- Very High altitude = 3500m – 5500m
- Extreme altitude = 5500m – above
- Troposphere — 8 km (above poles) – 18 km (above equator).
- Tropopause
- Stratosphere — 10km (above poles) 50 km (above equator),contains the Ozone layer
- Mesosphere — 50 km – 80 km
- Thermosphere — 100–200 km (1000°–1500° K)
- Exosphere — 500 km – 10,000km (outer space)

Altitude records


- 19 September, 1783 — 500m (1,700ft) animal carrying Montgolfier hot-air balloon.
- 15 October, 1783 — 26m (84ft) Pilâtre de Rozier in a Montgolfier tethered balloon.
- 1 December, 1783 — 2.7km Professor Charles and assistant Robert in Charliere, his hydrogen-filled balloon.
- 1784 — 4km Pilâtre de Rozier and the chemist Proust in a Montgolfier.
- 18 July, 1803 — 7.28km Etienne Gaspar Robertson and Lhoest in a balloon.
- 1839 — 7.9km Charles Green and Spencer Rush in a free balloon.
- 5 September, 1862 — 9km Coxwell and English physicist Glaisher in a balloon.
- 4 December, 1894 — 9.155km German meteorologist Berson in an airship.
- 31 July, 1901 — 10.8km German meteorologist Berson and Süring in a free balloon.

See also


- Altitude sickness ja:高さ simple:Height

Trajectory

A trajectory is an imagined trace of positions followed by an object moving through space. Some common examples of trajectories: (i) the path taken by a falling body, and (ii) the orbit of a spacecraft. A particular trajectory may be described mathematically either by the geometry of the entire trajectory (i.e. the set of all positions taken by the object), or as the position of the object as function of time. A familiar example is a projectile launched under the influence of only a uniform gravitational force field. A rock thrown on the practically airless surface of the Moon is a good approximation. In this case, the trajectory takes the shape of a parabola, provided the rock is not thrown too far. More generally, the precise trajectory of a projectile requires taking into account nonuniform gravitational forces and other forces such as drag and wind. This is the focus of the discipline of ballistics. A projectile, such as a baseball, when thrown through the air, is influenced by both gravity and aerodynamics. More generally, trajectory refers to the ordered set of intermediate states assumed by a dynamical system as a result of time evolution. The word trajectory is also often used metaphorically, for instance, to describe an individual's career.

Physics of trajectories

One of the remarkable achievements of Newtonian mechanics was the derivation of the laws of Kepler, in the case of the gravitational field of a single point mass (representing the Sun). The trajectory is a conic section, like an ellipse or a parabola. This agrees with the observed orbits of planets and comets, to a reasonably good approximation. Although if a comet passes close to the Sun, then it is also influenced by other forces, such as the solar wind and radiation pressure, which modify the orbit, and cause the comet to eject material into space. Newton's theory later developed into the branch of theoretical physics known as classical mechanics. It employs the mathematics of differential calculus (which was, in fact, also initiated by Newton, in his youth). Over the centuries, countless scientists contributed to the development of these two disciplines. Classical mechanics became a most prominent demonstration of the power of rational thought, i.e. reason, in science as well as technology. It helps to understand and predict an enormous range of phenomena. Trajectories are but one example. Consider a particle of mass m, moving in a potential field V. Physically speaking, mass represents inertia, and the field V represents external forces, of a particular kind known as "conservative". That is, given V at every relevant position, there is a way to infer the associated force that would act at that position, say from gravity. Not all forces can be expressed in this way, however. The motion of the particle is described by the second-order differential equation : m \frac = -\nabla V(\vec(t)) with \vec = (x, y, z) On the right-hand side, the force is given in terms of \nabla V, the gradient of the potential, taken at positions along the trajectory. This is the mathematical form of Newton's second law of motion: mass times acceleration equals force, for such situations.

Example: Uniform gravity, no drag or wind

The case of uniform gravity, disregarding drag and wind, yields a trajectory which is a parabola. To model this, one chooses V = m g z, where g (gee) is the so-called acceleration of gravity. This gives the equations of motion : \frac = \frac = 0 : \frac = - g Simplifications are made for the sake of studying the basics. The actual situation, at least on the surface of Earth, is considerably more complicated than this example would suggest, when it comes to computing actual trajectories. By deliberately introducing such simplifications, into the study of the given situation, one does, in fact, approach the problem in a way that has proved exceedingly useful in physics. The present example is one of those originally investigated by Galileo Galilei. To neglect the action of the atmosphere, in shaping a trajectory, would (at best) have been considered a futile hypothesis by practical minded investigators, all through the Middle Ages in Europe. Nevertheless, by anticipating the existence of the vacuum, later to be demonstrated on Earth by his collaborator Evangelista Torricelli, Galileo was able to initiate the future science of mechanics. And in a near vacuum, as it turns out for instance on the Moon, his simplified parabolic trajectory proves essentially correct. Relative to a flat terrain, let the initial horizontal speed be v_h, and the initial vertical speed be v_v. It will be shown that, the range is 2v_h v_v/g, and the maximum altitude is /2g. The maximum range, for a given total initial speed v, is obtained when v_h=v_v, i.e. the initial angle is 45 degrees. This range is v^2/g, and the maximum altitude at the maximum range is a quarter of that.

Derivation

The equations of motion may be used to calculate the characteristics of the trajectory. Let: :t \; be the time into the flight of the projectile :d_h(t) \; be the horizontal displacement at time t :d_v(t) = z \; be the vertical displacement at time t :v_h \; be the horizontal velocity (which is constant) :v_v \; be the initial vertical velocity upwards :v \; be the initial speed :v_v(t) \; be the vertical velocity at time t Along the horizontal dimension, v_h is a constant and thus by the equations of motion, :d_h(t)=v_h t \; (Equation 1) The vertical distance, or altitude follows the equations of motion for constant negative acceleration g: :d_v=v_vt- (Equation 2) :v_v = \frac d_v(t) = v_v-gt (Equation 3: velocity equation which is the derivative of equation 2) The range of the projectile occurs when d_v(t) is zero again and intercepts the ground. This occurs when d_v in equation 2 is zero: :0=v_vt- Solving this for time t gives the time of the projectile's flight: :t= (Equation 4: "hang time" of projectile) The maximum range occurs when equation 4 is substituted into equation 1: :d_h(t) = = = (Equation 5: range of projectile) The maximum altitude for a given trajectory occurs when the vertical velocity is zero. Thus set equation 3 to zero: :0=v_v-gt \; Solving for t :t= This can be substituted into equation 2 to give the maximum altitude: :d_v(max)=v_v ( ) - \frac 1 2 g( )^2 = (Equation 6: maximum altitude of projectile) Thus, not surprisingly, for a given initial speed the attained altitude is highest if the initial velocity was straight up. This altitude is twice the attained altitude when the range is maximized.

Derivation in polar coordinates

In terms of angle of elevation \theta and initial speed v: :v = \sqrt :v_h=v \cos \theta \; :v_v=v \sin \theta \; Substituting into Equation 1 gives: :d_h=v_h t = vt \cos \theta \; (Equation 1a) Substituting into Equation 2 gives: :d_v=v_vt- = ( v \sin \theta ) t - (Equation 2a) Taking the derivative gives the vertical velocity: :v_v=\frac d_v = \frac (v \sin \theta) t - = v \sin \theta -gt (Equation 3a: vertical velocity) Hang time calculated above in equation 4 may be expressed in terms of angle of elevation: :t= = (Equation 4a) Equation 4a may be substituted into Equation 1a to get the horizontal distance or range: :d_h=v_h t = =v () \cos \theta = Now using the trigonometric identity for 2 \sin \theta \cos \theta = sin 2 \theta: :d_h= (Equation 5a: range of projectile) This may be solved for angle \theta to give the "angle" equation to hit a target at range d_h: : = \frac 1 2 \sin^ ( ) (Equation 7: angle of projectile launch) Note that the sine function is such that there are two solutions for \theta for a given range d_h. Physically, this corresponds to a direct shot versus a mortar shot up and over obstacles to the target. The maximum altitude for a given range may be determined by setting the vertical velocity to zero in equation 3a and solving for t: :0= v \sin \theta -gt \; :t= \frac (rearrange and solve for t) Now substitute into the vertical height equation 2a: :d_v = (v \sin \theta) t - \frac = (v \sin \theta)(\frac ) - \frac = \frac - \frac = \frac (Equation 6a: max altitude for a given launch angle)

Maximum range

Given the above range and altitude equations, the maximum range and altitude may be determined. Both equations for the range, equations 5 and 5a may be used to determine the maximum range by setting their derivatives to zero. For equation 5, range of the projectile is a function of v_h and v_v such that v_v^2+v_h^2=v^2 where v is the total initial velocity and is constant. Thus, the range may be expressed as a function of v_v by solving for v_h: :v_h=\sqrt (Equation 8) And substituting v_h into equation 5: :d_h= = The maximum d_h may be determined by calculating the derivative and setting it to zero. The derivative is calculated as follows: :\frac d_h= \frac ::= (2 \sqrt +2v_v \frac \sqrt (application of product rule) ::= (2 \sqrt +2v_v \frac \frac) (application of chain rule) ::= (2 \sqrt +2v_v (\frac ) 2v_v) (derivative of square root) ::= (2 \sqrt - \frac) (simplify second term) Set to zero and solve for v: :0= (2 \sqrt - \frac) :\sqrt=\frac :v^2-^2=v_v^2 :v^2=2v_v^2 (Equation 9) Thus maximum range occurs when v^2 is 2v_v^2 and this can be substituted back into equation 8: :v_h=\sqrt=\sqrt=\sqrt=v_v Thus the maximum range occurs when v_h=v_v. The actual maximum range may now be calculated by substituting v_h=v_v and equation 9 into equation 5: :d_h = = = =

Maximum range in polar coordinates

The same conclusion may be drawn by starting with equation 5a. :\frac d_h = \frac ::= \frac \frac \sin 2 \theta \frac (application of chain rule) ::= \frac (\cos 2 \theta) 2 \quad Set to zero and solve for \theta: :0= \frac (\cos 2 \theta) 2 :0=\cos 2 \theta \quad Now cosine is zero at \pi \over 2: :2 \theta=\frac \pi 2 (also directly clear from equation 5a, it gives the maximum possible sine value of 1) :_ = \frac \pi 4 radians Thus the maximum range occurs when the angle is 45 degrees. The actual maximum range may now be calculated by substituting 45 degrees into equation 5a: :d_h== =

Maximum altitude at maximum range

Equations 6 and 6a may be used to calculate the maximum altitude at the maximum range. Equation 9 may be substituted into equation 6: :d_v=\frac=\frac=\frac Likewise 45 degrees may be substituted into equation 6a: :d_v=\frac=\frac=\frac

As a parabola

Equations 1 and 2 are parametric equations that describe a parabola. They may be rearranged into the more familiar quadratic form by solving equation 1 for t and substituting into equation 2: :t=\frac (rearrange equation 1 for t) Substituting this into equation 2: :d_v=v_vt- \frac=v_v(\frac)-\frac=-\frac(d_h)^2 + \frac(d_h) This is now in the form :y=ax^2+bx+c \quad where :y=d_v, x=d_h, a=-g/, b=v_v/v_h, c=0. This is the form of a parabola and thus the trajectory is a parabola. Likewise equations 1a and 2a can be rearranged into quadratic form. Equation 1a may be rearranged to: :t=\frac And this may be substituted into equation 2a: :d_v=vt \sin \theta - \frac=v \sin \theta \frac - \frac Now \tan \theta=\sin \theta / \cos \theta, so: :d_v=-\fracd_h^2 + d_h \tan \theta (Equation 10) This is again now in the form y=ax^2+bx+c where y=d_v, x=d_h, a=-g/, b=\sin \theta / \cos \theta and c=0 demonstrating that this is a parabola. The quadratic formula gives the location of the intersection of the parabola and the x-axis. This is where the projectile trajectory starts and ends and thus may be used directly to calculate the range. In terms of rectilinear coordinate systems: : d_h=\frac=\frac = \frac=0, \frac This is the same result as equation 5 above. In polar coordinates and using the trigonometric identity 2 \sin \theta \cos \theta = \sin 2 \theta, the intersections are: : d_h=\frac=\frac =0, \frac = 0, \frac = 0, \frac This is the same result as in equation 5a above. Similarly, the vertex of the parabola is the maximum altitude for a given range.

Uphill/downhill in uniform gravity in a vacuum

Given a hill angle \alpha and launch angle \theta as before, it can be shown that the range along the hill R_s forms a ratio with the original range R along the imaginary horizontal, such that: :\frac =(1-\tan \theta \tan \alpha)\sec \alpha (Equation 11) In this equation, downhill occurs when \alpha is between 0 and -90 degrees. For this range of \alpha we know: \tan(-\alpha)=-\tan \alpha and \sec ( - \alpha ) = \sec \alpha. Thus for this range of \alpha, R_s/R=(1+\tan \theta \tan \alpha)\sec \alpha . Thus R_s/R is a positive value meaning the range downhill is always further than along level terrain. This makes perfect sense as it is expected that gravity will assist the projectile, giving it greater range. While the same equation applies to projectiles fired uphill, the interpretation is more complex as sometimes the uphill range may be shorter or longer than the equivalent range along level terrain. Equation 11 may be set to R_s/R=1 (i.e. the slant range is equal to the level terrain range) and solving for the "critical angle" \theta_: :1=(1-\tan \theta \tan \alpha)\sec \alpha \quad \; :\theta_=\arctan((1-\csc \alpha)\cot \alpha) \quad \; Equation 11 may also be used to develop the "rifleman's rule" for small values of \alpha and \theta (i.e. close to horizontal firing, which is the case for many firearm situations). For small values, both \tan \alpha and \tan \theta have a small value and thus when multiplied together (as in equation 11), the result is almost zero. Thus equation 11 may be approximated as: :\frac =(1-0)\sec \alpha And solving for level terrain range, R :R=R_s \cos \alpha \ "Rifleman's rule" Thus if the shooter attempts to hit the level distance R, s/he will actually hit the slant target. "In other words, pretend that the inclined target is at a horizontal distance equal to the slant range distance multiplied by the cosine of the inclination angle, and aim as if the target were really at that horizontal position."[http://www.snipertools.com/article4.htm]

Derivation based on equations of a parabola

The intersect of the projectile trajectory with a hill may most easily be derived using the trajectory in parabolic form in Cartesian coordinates (Equation 10) intersecting the hill of slope m in standard linear form at coordinates (x,y): :y=mx+b \; (Equation 12) where in this case, y=d_v, x=d_h and b=0 Substituting the value of d_v=m d_h into Equation 10: :m x=-\fracx^2 + \frac x :x=\frac(\frac-m) (Solving above x) This value of x may be substituted back into the linear equation 12 to get the corresponding y coordinate at the intercept: :y=mx=m \frac (\frac-m) Now the slant range R_s is the distance of the intercept from the origin, which is just the hypoteneuse of x and y: :R_s=\sqrt=\sqrt ::=\frac \sqrt ::=\frac (\frac-m) \sqrt Now \alpha is defined as the angle of the hill, so by definition of tangent, m=\tan \alpha. This can be substituted into the equation for R_s: :R_s=\frac (\frac-\tan \alpha) \sqrt Now this can be refactored and the trigonometric identity for \sec \alpha = \sqrt may be used: :R_s=\frac(1-\frac\tan\alpha)\sec\alpha Now the flat range R=v^2\cos 2 \theta / g = 2v^2\cos\theta\sin\theta by the previously used trigonometric identity and \sin\theta/\cos\theta=tan \theta so: :R_s=R(1-\tan\theta\tan\alpha)\sec\alpha \; :\frac=(1-\tan\theta\tan\alpha)\sec\alpha

See also


- Planetary orbit
- Orbit (dynamics)
- Orbit (group theory)
- Equation of motion
- Rigid body Category:Ballistics Category:Mechanics

18 February

February 18 is the 49th day of the year in the Gregorian Calendar. There are 316 days remaining (317 in leap years).

Events


- 3102 BC - Epoch (origin) of the Kali Yuga- Lord Krishna leaves his mortal coil.
- 1229 - The Sixth Crusade: Frederick II, Holy Roman Emperor signs a ten-year truce with al-Kamil, regaining Jerusalem, Nazareth, and Bethlehem with neither military engagements nor support from the papacy.
- 1478 - George, Duke of Clarence, convicted of treason against his older brother Edward IV of England, is privately executed in the Tower of London.
- 1685 - Fort St. Louis is established by a Frenchman at Matagorda Bay thus forming the basis for France's claim to Texas.
- 1797 - Trinidad is surrendered to a British fleet under the command of Sir Ralph Abercromby.
- 1814 - Battle of Montereau occurs.
- 1841 - The first ongoing filibuster in the United States Senate begins and lasts until March 11.
- 1856 - The American Party (Know-Nothings) convene in Philadelphia, Pennsylvania to nominate their first Presidential candidate, former President (Millard Fillmore).
- 1861 - In Montgomery, Alabama Jefferson Davis is inaugurated as the provisional President of the Confederate States of America.
- 1861 - With the Italian unification almost complete, King Victor Emmanuel II of Piedmont, Savoy and Sardinia assumes the title of King of Italy.
- 1865 - In the U.S., Delaware voters reject the 13th Amendment to the U.S. Constitution, and vote to continue the practice of slavery. (Delaware finally ratifies the amendment on February 12, 1901.)
- 1878 - The Lincoln County War begins in Lincoln County, New Mexico.
- 1885 - Mark Twain's Adventures of Huckleberry Finn is published for the first time.
- 1911 - The first official flight with air mail takes place in Allahabad, British India, when Henri Pequet, a 23-year-old pilot, delivers 6,500 letters to Naini, about 10 km away.
- 1913 - Raymond Poincaré becomes President of France.
- 1929 - First Academy Awards are announced.
- 1930 - While studying photographs taken in January, Clyde Tombaugh discovers Pluto.
- 1930 - Elm Farm Ollie becomes the first cow to fly in an airplane and also the first cow to be milked in an airplane.
- 1932 - The Empire of Japan declares Manzhouguo (obsolete Chinese name for Manchuria) independent from China.
- 1943 - The Nazis arrest the members of the White Rose movement.
- 1943 - Joseph Goebbels delivers the Sportpalast speech
- 1948 - Eamon de Valera resigns as Taoiseach of Ireland.
- 1953 - The first 3D film, Bwana Devil, opens.
- 1953 - Lucille Ball and Desi Arnaz sign an $8,000,000 contract to continue the I Love Lucy television series through 1955.
- 1965 - The Gambia becomes independent from the United Kingdom.
- 1970 - The Chicago Eight are found not guilty of conspiring to incite riots at the 1968 Democratic Party national convention.
- 1972 - The California Supreme Court invalidates the state's death penalty and commutes the sentences of all death row inmates to life in prison.
- 1974 - The game show Tattletales debuts in the slot vacated by the long-running soap opera The Secret Storm.
- 1974 - KISS releases their self-titled debut album.
- 1977 - The Space Shuttle Enterprise test vehicle goes on its maiden "flight" while sitting on top of a Boeing 747.
- 1983 - Thirteen people die and one is seriously injured in the Wah Mee Massacre in Seattle, Washington, said to be the largest robbery-motivated mass-murder in American history.
- 1985 - The legendary "mirror globe" ident, first used in 1969, is seen for the last time in regular rotation on BBC1.
- 1998 - Two white separatists are arrested in Nevada and accused of plotting a biological attack on New York City subways.
- 2003 - Nearly 200 people die in the Daegu subway fire in South Korea
- 2004 - Up to 295 people, including nearly 200 rescue workers, die near Neyshabur in Iran when a run-away freight train carrying sulfur, petrol and fertiliser catches fire and explodes.
- 2005 - The United Kingdom law banning fox hunting, hare coursing and other sports which kill wild mammals is enforced from this date.

Births


- 1516 - Queen Mary I of England (d. 1558)
- 1530 - Uesugi Kenshin, Japanese samurai and warlord (d. 1578)
- 1559 - Isaac Casaubon, French classical scholar (d. 1614)
- 1602 - Per Brahe (the younger), Swedish soldier and statesman (d. 1680)
- 1635 - Johan Göransson Gyllenstierna, Swedish statesman (d. 1680)
- 1609 - Edward Hyde, 1st Earl of Clarendon, English statesman and historian (d. 1674)
- 1642 - Marie Champmeslé, French actress (d. 1698)
- 1658 - Charles-Irénée Castel de Saint-Pierre, French writer (d. 1743)
- 1745 - Alessandro Volta, Italian physicist (d. 1827)
- 1835 - César Cui, Lithuanian composer (d. 1918)
- 1838 - Ernst Mach, Austrian physicist and philosopher (d. 1916)
- 1846 - Wilson Barrett, English actor and playwright (d. 1904)
- 1848 - Louis Comfort Tiffany, American glass artist (d. 1933)
- 1849 - Alexander Kielland, Norwegian author (d. 1906)
- 1859 - Sholom Aleichem, Russian Yiddish humorist and author (d. 1916)
- 1871 - Harry Brearley, English inventor (d. 1948)
- 1883 - Nikos Kazantzakis, Greek writer (d. 1957)
- 1884 - Andrew Watson Myles, Canadian politician (d. 1970)
- 1890 - Edward Arnold, American actor (d. 1956)
- 1890 - Adolphe Menjou, American actor (d. 1963)
- 1892 - Wendell Willkie, U.S. Presidential candidate (d. 1944)
- 1896 - Andre Breton, French writer (d. 1966)
- 1898 - Enzo Ferrari, Italian race car driver and manufacturer (d. 1988)
- 1901 - Reginald Sheffield, British actor (d. 1957)
- 1903 - Nikolai Podgorny,